The invention relates to a method and apparatus for determining if an unfamiliar data point representing various parameters should be classified in a category (e.g. "acceptable"), given a population defined by known data points representing the same parameters, which known data points are considered to belong in that category with regard to those parameters.
The invention also has application in the field of color recognition (color analysis). Manufacturers of colored articles, for example, presently require pigment (or color dye) suppliers to provide samples of pigments to the manufacturer and/or to the buyer of the articles. A human being then visually determines which pigment is acceptable for the articles that the manufacturer is planning to manufacture. The pigment supplier then supplies the pigment to the manufacturer who then proceeds to manufacture the articles, possibly after first visually inspecting the pigment to ensure that it matches the sample. After the articles are manufactured, the finished article is again visually inspected for acceptability with regard to color. This is because during the manufacturing process, particularly if the process requires heat (such as in an injection molding process), an error in controlling the process may cause the color of the finished article to deviate from the desired color. The buyer of the finished article may also perform a visual inspection with regard to color. Each of the visual inspections performed before, during, and after the manufacture of the finished article involve subjectivity, and different color experts may have different opinions as to whether or not a colored article is acceptable with regard to color. Further, each visual inspection involves the cost of using a color expert.
The prior art provides algorithms for determining if a unfamiliar data point representing various parameters should be deemed "acceptable" given a population of data points that represent the various parameters and that have been determined to be "acceptable". With regard to color data points representing three parameters (for example, a red/green parameter (a*), a yellow/blue parameter (b*), and a lightness parameter (L*)), a prior art method for determining if an unfamiliar data point should be acceptable given a population of known acceptable data points would attempt to fit an ellipsoid around the known acceptable data points and would determine if the unfamiliar data point lies within the ellipsoid to determine if the unfamiliar data point should be acceptable. More particularly, since it is difficult to fit a three dimensional ellipsoid around known acceptable data points, the prior art method will usually define three ellipses, one in each of the three two-dimensional planes a*-b*, b*-L*, and a*-L*. The reason that an elliptical shape was used in the prior art method is that this shape takes into account the fact that a greater amount of deviation may be tolerable for one of the parameters than for another of the parameters. A problem with the prior art approach is that many known acceptable data points are required. The method will not work when there are only a few known acceptable data points. Another problem with this prior art approach is that the ellipsoid that is defined may include regions that would contain unacceptable data points.
Attention is directed to the following reference, which is incorporated herein by reference for background purposes, and which discusses some statistical techniques for solving classification problems:
Johnson, Richard A., and Dean W. Wichern, Applied Multivariate Statistical Analysis, Prentice Hall, Englewood Cliffs, N.J., Second Edition, pp. 470-531.
It should be noted that the techniques disclosed in Applied Multivariate Statistical Analysis generally are useful only for populations that are normally distributed.